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What is greatest positive integer n such that 2^n is a factor of 12^10

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What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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New post 27 Oct 2011, 00:06
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What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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New post 27 Oct 2011, 00:32
2
aselfmademan wrote:
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...


The given number is 12^10
=(2*2*3)^10
=(2^20)*(3^10)

So the greatest possible value for n such that 2^n can be factor of given number is 20.

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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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New post 27 Oct 2011, 05:02
3
aselfmademan wrote:
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...


\(12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}\)
The greatest value of n such that \(2^n\) is a factor of \(12^{10}\) is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that \(2^n\) is a factor of 12!
Try this one.
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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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New post 27 Oct 2011, 08:03
VeritasPrepKarishma wrote:
aselfmademan wrote:
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...


\(12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}\)
The greatest value of n such that \(2^n\) is a factor of \(12^{10}\) is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that \(2^n\) is a factor of 12!
Try this one.


Thank you very much.......... :-D I am very weak in this type of PS math :(
Could you please explain 12! math you have given ?
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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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New post 27 Oct 2011, 20:32
VeritasPrepKarishma wrote:
aselfmademan wrote:
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...


\(12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}\)
The greatest value of n such that \(2^n\) is a factor of \(12^{10}\) is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that \(2^n\) is a factor of 12!
Try this one.



n = 10

I just counted the number of 2s till 12 since the 12! is multiplication of all numbers till 12


Do you have any faster method which can be used for bigger factorials?
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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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New post 27 Oct 2011, 20:39
2
Check out this post: http://www.veritasprep.com/blog/2011/06 ... actorials/

It discusses how to solve such questions quickly.
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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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New post 07 Mar 2016, 09:36
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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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New post 02 Feb 2018, 11:28
Hi All,

This question comes down to exponent rules and how to 'rewrite' a number raised to a power.

12 = (2)(2)(3)

12^2 = (2^2)(2^2)(3^2) = (2^4)(3^2)
12^3 = (2^3)(2^3)(3^3) = (2^6)(3^3)

Seeing this pattern, you should be able to rewrite 12^10...

12^10 = (2^10)(2^10)(3^10) = (2^20)(3^10)

So the largest 'power of 2' that is a factor of 12^10 is 20.

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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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Re: What is greatest positive integer n such that 2^n is a factor of 12^10   [#permalink] 21 Jul 2019, 05:42
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